Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The software calculates hertzian contact stress and the subsurface stressen of the general contact of two elliptical bodies according to the hertzian theorie. This stillrelevant classical solution provides a foundation for modern problems in contact mechanics. Contact mechanics hertz stress constriction resistance asperities hertzian contact. Contact pressure and yield stress phoenix tribology.
Indentation depth may be readily compared using standard experimental apparatus. References 1 shailendra pipaniya, akhilesh lodwal, contact stress analysis of deep groove bearing 6210 using hertzian contact stress. Pdf contact stress distribution of deep groove ball. Hertzian static contact stress acceptance criteria. Hertz contact stress mechanical engineering general. A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies surfaces known as the normal direction and frictional stresses acting tangentially between the surfaces. In another failure mode, called contact or hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface. A clearly laidout window allows you to enter material properties, dimensions and loads. The hertzian theory has previously been used to describe the contact. The consequences for these limitations are small for optics and unless there is an argument that the stress must be known exact as possible, for optical engineers using the hertz contact theory as.
Contact fatigue differs from classic structural fatigue bending or torsional in that it results from a contact or hertzian stress state. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. The contact area will change depending on the magnitude of the contact stress. Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of hertzian contact stress equations can estimate maximum stresses produced and ways. Hertz contact stress calculations and graphs with hertzwin. Hertz in terms of the solution of a transcendental equation involving elliptic integrals and used by him to describe the deformation of bodies subjected to contact. Some features of this site may not work without it. The domain in this study was the angular location of the point of contact on the arc of. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a flat surface. The hypothesis of this work is that the contact mechanics of edgeloaded hip bearings can be accurately described using hertzian contact theory. The company was founded in 2011 and is majority owned by fouriertransform ab vicura, 20. To speed up the process of calculation and accurate the model, fischer et. We report on the elastic contact between a spherical lens and a patterned substrate, composed of an hexagonal lattice of cylindrical.
The domain in this study was the angular location of the point of contact on the arc of action from the beginning to the end of contact between this pair of teeth. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. Hertzian impact model and to quantitatively evaluate its limits. New version of hertzian contact stress calculation mesys ag. This kind of stress may not be significant most of the time, but may cause.
The future work of this paper will be the calculation of contact stress using different ball bearing materials and different sizes of bearings. Contact stresses and deformations curved surfaces in contact. Relation between hertz stresslife exponent, ballrace. Even though the derivation of the theory is relatively difficult, the final solution is a set of simple analytical equations relating the properties of the system to the developed stress. The description of functionality of rolling bearing calculation for slewing rings. Hertzian contact theory applied to edgeloaded ceramicon. A theoretical background to the hertz contact theory can be found here. Typically people denote maximum stress according to hertz contact theory as a hertz contact stress. Usually, hertz contact stresses are judged by the shear stress just below the surface. Impactgenerated vibrations were recorded with an array of pm sensitive high.
Hlim also allowable contact number this is the limit of rolling contact stress that the camsteel can sustain for ncycles, with a reliability of 99%, without failure by pitting. Hertz contact stress of deep groove ball bearing sciencedirect. The hertzian contact theory is approximated according to a concept by tanaka 2001, a new calculation method of hertz elliptical contact pressure, asme j. Considering the geometry of the contacting bodies first, the effect of the diameters on the contacting area is given by equation 1. You could divide the hertz stresses by the same factors before comparing them to your allowables. The hertz contact theory the hertz contact theory consists of a series of mathematical equations to calculate normal, hoop, radial, and shear stress components on and within a soft flat surface or halfspace, known as the specimen, when pressed by a. However, as the load increases, the hertzian model becomes inaccurate as well. This paper presents a systematic study of ball impact as a source of stress waves for a number of different material combinations. The contact pressure distribution between the ball and the raceway of the bearing 6004 is performed by finite element software. From fea modeling, materion developed an empirical calculator to approximate the maximum contact stress for a. The contact pressure is intensified near the pitch circle, where the contact is pure rolling with zero sliding velocity. Hertzwin is a free hertzian contact stress calculator. Contact between two continuous, nonconforming solids is initially a point or line. We consider the deformations in an elastic halfspace, which are caused by a given stress acting upon its.
Eccentricity of contact ellipse e b a r r b a 2 2 4 3 11. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained. Cooper abstract formulations are given for the coefficients x, u, u defined by h. For these to be true, it is assumed that the contact is elastic, that the contact zone is flat, that there are no shear stresses in the contact zone and that the contact. When applicable, the hertz theory can be used to accurately model contact dimensions, normal pressures, and stress fields. A brief discussion of what affects hertz stress, and why in connector design even if hertz stress itself is not. A practical and accurate formulation is still in demand 2. In 1882, hertz solved the contact problem of two elastic bodies with curved surfaces. Hertzian contact stress allowable hertzian contact stress transverse pressure angle operating pressure angle base helix angle angular velocity. In case of two cylinders in contact with radii, as shown in fig. Contact stress has been expressed clearly in this work by finite element model.
For these to be true, it is assumed that the contact is elastic, that the contact zone is flat, that there are no shear stresses in. Pdf hertzian contact stress calculator ames dennyza. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. An approximate analysis for hertzian elliptical wheelrail. Hertz contact stress theory allows for the prediction of the resulting contact area, contact pressure, compression of the bodies, and the induced stress in the bodies. Apr 22, 20 step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. Assessment of the applicability of hertzian contact theory to. Hertzian contact stress forms the foundation for the equations for load bearing capabilities and fatigue. Pdf hertz contact stress analysis and validation using finite. Under the action of a load the solids deform and a contact area is formed as shown in figure 1. These elevated stresses are beyond the hertzian field. But yes, in static cases you can often allow for higher stress.
Nicholas lecain, tutorial of hertzian contact stress analysis, opti 521, college of optical sciences, university of arizona, tucson, az. Contact stress analysis of spur gear for different. Contact stress analysis of spur gear for different materials. Gear tooth surface wear involves removal or displacement of. Therefore, it is very imporant to calculate the actual stress at the point of contact, the socalled contact stress by theory of elasticity, developed by hertz, in 1881, when he was 23 years old. Another contact case entails friction that causes shear stresses on the contact zone. A brief discussion of what affects hertz stress, and why in connector design even if hertz stress. The next issue of technical tidbits will discuss stress relaxation. The hertzian contact stress contactstresses lead to octahedral shearstress and orthogonal shearstresses under the surface at the contact.
It can be used to calculate mechanical point and line contact dimensions and material stresses. Assessment of the applicability of hertzian contact theory. Pdf hertz contact stress analysis and validation using. Nov 15, 2008 an example of hertz contact fem simulation. Contact hertz stress the contact hertz stresses at the respective races of a bearing are a function of the bearing geometry, the normal load at the contact, and the elastic properties of the bearing materials. The application performs all calculations automatically. Pdf contact stress analysis in wheelrail by hertzian. Figure c1 shows the relationship between the load p and the maximum shear stress that occurs just below the surface. Pdf rigorous treatment of contact problems hertzian contact. From contact mechanics2 demonstrating the change in area during conditions of load. Introduction basic knowledges elastic contact inelastic contact contact of composites. Hertzian contact stress theory university of arizona.
Hertzian stress between the two cylindrical contact surfaces. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. Step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. In this case, we can consider a small area of the contact region da, fig. There the elastohydrodynamic oil film is minimal and the load is less distributed. Using trescas criterion, a minimum yield stress of 422 nmm2 will be required for ductile materials. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. This paper examines the contact stress distribution of deep groove ball bearings through analytical and numerical methods. Contact stress analysis of spur gear ijert journal. However, it is nevertheless of interest to examine these predictions either by experiment or by independent computation. It is tempting to accept the predictions regarding indentation depth and radius of circle of contact between two elastic bodies in contact given by the wellknown hertz equations at face value. Contact stress causes deformation, plastic or elastic.
Contact mechanics is the study of the deformation of solids that touch each other at one or more. We consider the deformations in an elastic halfspace, which are caused by a given stress acting upon its surface. The crucial requirement of effective power transmission in various machines, automobiles, elevators, generators, etc has created an increasing demand for more accurate analysis of the characteristics of gear systems. We can also do wear analysis due to frictional rubbing between the contact surfaces. Although hertzian contact theory has been applied in the case of concentric ceramiconceramic hip contact mak and jin, 2002, its merits and shortcomings have not been assessed in abnormal states and multiple material couples. Tables of hertzian contactstress coefficients welcome to the ideals repository. In this case, we can consider a small area of the contact region. Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. In many cases, the resultant stresses are not of design significance, but in some cases failure can. Me en 7960 precision machine design contact stresses and deformations.
The tensile stress at the major radius sa is maximum. The contact pair topology influences the contact stress magnitude and shape of contact area. These stresses can then be analyzed in context of the application. The image to the left schematically illustrates how a cylinder rolling over a flat body in the absence of friction develops subsurface stresses.
This page focuses mainly on the normal direction, i. Hertz in terms of the solution of a transcendental equation involving elliptic integrals and used by him to describe the deformation of bodies subjected to contact stresses. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately. Nov 10, 2011 although hertzian contact theory has been applied in the case of concentric ceramiconceramic hip contact mak and jin, 2002, its merits and shortcomings have not been assessed in abnormal states and multiple material couples.
The contactpair topology influences the contact stress magnitude and shape of contact area. Tables of hertzian contactstress coefficients duane h. Stresses formed by the contact of two radii can cause extremely high surface stresses. Useful solutions to standard problems in introduction and synopsis modelling is a key part of design. This condition is modeled as a pair of cylinders in line contact, and a hertzian contact stress. If the pressure is integrated over the contact area, it is found that 3f pmax 2nab 3. The ellipticity parameter k can be written in terms of. The hertzian contact stress contact stresses lead to octahedral shear stress and orthogonal shearstresses under the surface at the contact. For example, in mechanical engineering and tribology, hertzian contact stress is a description of the stress within mating parts. This provides an accurate value of the contact pressure at low loads. The application of hertzian contact stress equations can estimate maximum stresses produced. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties which maximize performance. Vicura ab is an engineering company that delivers products which are used in.
Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of hertzian contact stress equations can estimate. Hertzian contact equations for elliptical, spherical and. Stress concentration in periodically rough hertzian contact. The term failure from pitting fatigue is subjective and a source of considerable disagreement. Hertzian cone, the cone produced when an object passes through a solid, such as a bullet through glass. Hertzian dipole, defined as a finite oscillating current over an infinitesimal length at a specified position. A new version of the software for calculation of hertzian contact stress is available. Contact fatigue has been identified in metal alloys both ferrous and nonferrous and in ceramics and cer mets. Conditions are therefore small deformations in regard to the radii of curvature and pure elastic. These contact stresses are called hertz contact stresses, which was first studies. Contact pressure and yield stress in the case of point contacts round or elliptical that we may not be justified in using the hertzian contact equations. The hertz contact theory consists of a series of mathematical equations to calculate normal, hoop, radial, and shear stress components on and within a soft flat surface or halfspace, known as the specimen, when pressed by a rigid hemisphere called the indentor appendix figure 1 1.
This tutorial addresses the basics of hertzian contact stress. Contact stress reduction mechanisms for the cambased. Tutorial on hertz contact stress university of arizona. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces. Spheres in contact vertical stress distribution at center of contact area plot shows material with poissons ratio. Hertzian contact stress, localized stresses that develop as two curved surfaces come in contact and deform slightly under imposed loads. Indentation depth may be readily compared using standard experimental. Introduction when there are two nonconforming surfaces that come into contact the point or line of contact can be a location of very high stress values.
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